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unique number





The constant Un that results if a number An consisting of n consecutive digits, in ascending order, is subtracted from the number An' obtained by reversing the digits of An. For example, a three-digit number 345, if subtracted from its reverse 543, yields a difference of 198. Any other three-digit number subtracted from its reverse gives the same difference. Thus U3 = 198. Similarly for a number with four consecutive digits, the unique number U4 = 3087. The first ten unique numbers are: U1 = 0, U2 = 9, U3 = 198, U4 = 3087, U5 = 41976, U6 = 530865, U7 = 6419754, U8 = 75308643, U9 = 864197532, and U10 = 9753086421. Unique numbers are related to Kaprekar numbers, Kn, by the formula
Un + Un' = Kn + Kn'.
For example, when n = 4, K4 = 6174, K4' = 4716, U4 = 3087, U4' = 7803, and
3087 + 7803 = 10890 = 6174 + 4716.

Reference

  1. Gupta, S. S. "Unique Numbers", Science Today, January 1988, India.

External site

Shyam Sunder Gupta (unique numbers)


Related category

   • TYPES OF NUMBERS